Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22581508 | C2 | semidirect |
| 3. #22581287 | C2 | semidirect |
| 4. #22581234 | C2 | semidirect |
| 5. #22581233 | C2 | semidirect |
| 6. #22581155 | C2 | semidirect |
| 8. #22581056 | C2 | semidirect |
| 9. #22581054 | C2 | semidirect |
| 10. #22581009 | C2 | semidirect |
| 11. #461×C139 | C2 | semidirect |
| 15. #17984842 | C22 | semidirect |
| 19. Q8×Dic139 | C22 | semidirect |
| 30. #17984776 | C22 | semidirect |
| 31. #17984775 | C22 | semidirect |
| 32. C4⋊(C139⋊C8) | C22 | semidirect |
| 33. #17984766 | C22 | semidirect |
| 37. #17984752 | C22 | semidirect |
| 39. C4⋊Q8×C139 | C22 | semidirect |
| 41. C4⋊C8×C139 | C22 | semidirect |
| 42. #103×C139 | C22 | semidirect |
| 146. C139 | #3110 | semidirect |
| 154. #461 | D139 | semidirect |
| 164. C4⋊Q8 | C2×D139 | semidirect |
| 183. C4⋊C8 | C2×D139 | semidirect |
| 185. #103 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581508 | 2 |
| C4×D4×D139 | 2 |
| #22581287 | 2 |
| #22581234 | 2 |
| #22581233 | 2 |
| #22581155 | 2 |
| #22581102 | 2 |
| #22581056 | 2 |
| #22581054 | 2 |
| #22581009 | 2 |
| #461×C139 | 2 |
| #3110 | 139 |